184 THE MATHEMATICAL THEORIES OF THE EARTH. 



important ])arts of inatliomatical litoi ature. In its dynamical and phys- 

 ical aspects tlie Earth was to them the i)rincipal object of research, and 

 the thoronghness and completeness of their contributions toward an ex- 

 l)lanation of the " system of the world " are still a source of wonder and 

 admiration to all who take the trouble to examine their works. 



A detailed discussion of the known properties of the earth, and of 

 the hypotlieses concerning the unknown properties, is no fit task for a 

 summer afternoon ; the intricacies and delicacies of the subject are suit- 

 able only for another season and a special audience. But it has seemed 

 that a somewhat popular review of the state of our mathematical knowl- 

 edge of the Earth might not be without interest to those already famil- 

 iar with the complex details, and might also help to increase that gen- 

 eral interest in science, the promotion of which is one of the most 

 important fujictions of this association. 



As we look back through the light of modern analysis, it seems 

 strange that the successors of jSTewton, who took up the problem of the 

 shape of the Earth, should have divided into hostile camps over the 

 question whether ourplanetis elongated or flattened atthe poles. They 

 agreed in the opinion that the Earth is a spheroid, but they debated, 

 investigated, and observed for nearly half a century before deciding 

 that the sjdieroid is oblate rather than oblong. This was a critical 

 question, and its decision marks perhaps the most important epoch in 

 the history of the figure of the Earth. The Newtonian view of the oblate 

 form found its ablest supporters in Huygens, Maupertuis, and Clair- 

 aut, while the erroneous view was maintained with great vigor by the 

 justly distinguished Cassinian school of astronomers. Unfortunately 

 for the Cassinians, defective measures of a meridional arc in France 

 gave color to the false theory and furnished one of the most con- 

 spicuous instances of the deterring efiect of an incorrect observa- 

 tion. As you well know, the point was definitely settled by Mauper- 

 tuis's measurement of the Lapland arc. For this achievement his name 

 has become famous in literature as well as in science, for his friend 

 Voltaire congratulated him on having " flattened the poles and the 

 Cassinis;" and Carlyle has honored him with the title of " Earth-flat- 

 teuer." * 



Since the settlement of the question of the form — i)rogress toward 

 a knowledge of the aize of the Earth has been consistent and steady, 

 until now it may be said that there are few objects with which we have 

 to deal whose dimensions are so well known as the dimensions of the 

 Earth. But this is a popular statement, and like most such, needs to 

 be explained in order not to be misunderstood. Both the size and 

 shape of the Earth are defined by the lengths of its e()uatorial and ])olar 

 axes; and, knowing the fact of the oblate spheroidal form, the lengths 

 of the axes may be found within narrow liniits from simple measure- 



*Toilbunter, Hiatort/ of the Theories of Attraction and the Figure of the Earth. 

 Loiuloii, lf^73, vol. 1, art. 19r>. 



